关于函数级数一致收敛的判别法  

On Criterion of Uniform Convergence of Functian Series

作　　者：陈治友 

机构地区：[1]贵阳师专数学系,贵阳550008

出　　处：《贵州大学学报（自然科学版）》1996年第4期243-247,共5页Journal of Guizhou University:Natural Sciences

摘　　要：本文阐明的是关于函数级数一致收敛的判别法,我们知道,当我们取消阿贝尔判别法中函数列{a_m(n)}的单调性后,阿贝尔判别法是难以成立的,但当我们给出函数列{a_n(x)}与函数级数 sum from m=1 to ∞b_m(x)仍然一致收敛,最后通过对一个例题的讨论说明本文所述的判虽法与文中的三种判别法(狄利克莱判别法,阿贝尔判别法,M-判别法)之异同。Generally,the ABel's critrion not has to be true when we cancel soe coaditions.But when sequence of function{a_n(x)}and funetion series sum from n=1 to ∞ b_n(x)satisfy the other condi- tions.We can prove that function series sum from n=1 to ∞ a_n(x)b_n(x)is uniform convergence. In the other hand,We can prove that this criterion is different from three criterions in the reference book.

关 键 词：一致收敛 判别法 函数级数 阿贝尔判别法 

分 类 号：O171[理学—数学]